J . A m . Chem. SOC.1982, 104, 7501-7509
7501
Electron Deformation Density for the “Supershort” C r A C r Bond: A Joint Experimental and Theoretical Study Andre Mitschler,IaBernard Rees,*laVcRoland Wiest,lb and Marc BenardIb Contribution from ER 139 du CNRS and UniuersitG Louis Pasteur, 67070 Strasbourg CCdex, France. Received May 18, 1982
Abstract: The charge density distribution in “supershort” metal-metal quadruple bonds has been investigated both experimentally in tetrakis(p-2-hydroxy-6-methylpyridine)dichromium [ C r , ( m h ~ ) ~and ] theoretically in tetrakis(p-dimethylphosphoniumylidenedimethy1ido)dichromium. The two compounds have similar molecular structures and practically identical Cr-Cr bond lengths (1.879 and 1.885 A, respectively). Three low-temperature (74 K) X-ray data sets were collected on Cr2(mhp),: one high-order set was used to determine the atomic positional and thermal parameters, and two sets with a maximum resolution 2(sin O)/A of 1.52 k’ were used to compute the charge density. A systematic bias having been detected (and later on corrected) in one of those, the effect of systematic error on the final deformation density maps is discussed. The quantum-chemical LCAO calculations were performed ab initio with configuration interaction. The experimental and theoretical deformation density maps are qualitatively very similar. The most striking feature is a strong charge density accumulation between the Cr atoms, with a maximum at the bond midpoint and an extension over the K and 6 regions. The peak height (experimental, 0.4; theoretical, 0.3 e A-3) is comparable to deformation density peaks between first-row atoms. A comparison is performed with experimental and theoretical density distributions previously obtained for dichromium and dimolybdenum tetracarboxylates. An analysis of the computed maps leads to the definition of a “quadruple-bond pattern” remaining qualitatively similar over a very large range of metal-metal distances.
Introduction
erratically than the chromium analogues; for example, the range of the Mo-Mo bond length is much narrower. An ab initio S C F calculation7 showed that a27r46, is the ground state, and a limited C I calculation gave a weight of 66% to the leading term u2a462, while for chromium formate3 it was only 18%.* This difference in bonding corresponds to differences in the charge density distribution, as established by the two experimental determinations. In both cases the density is near zero on the metal-metal bond axis, but a torus of positive residual density is seen around this axis in the molybdenum compound while in the chromium compound a very shallow and slightly positive residue is spread out over a large region. We report here the results of a low-temperature determination of charge distribution by X-ray diffraction (“X-X” method) in a compound with a supershort Cr-Cr bond: tetrakis(h-2hydroxy-6-methylpyridine)dichromium, or Cr2(mhp),. The structure of this compound, crystallized with one molecule of CH2C1,, has been determined by X-ray diffraction by Cotton et
In recent years a large number of quadruply bonded Cr-Cr compounds have been synthesized. This class of compounds presents some rather puzzling characteristics, in particular, the large range of the metal-metal bond lengths, which varies over as much as 0.7 A.2 Such large differences indicate that behind the formal concept of quadruple bonding the real bonding situations may be quite different. Theoretical investigations on dichromium tetraformate3 have shown that neither the “pure quadruple bond” a2a46, nor the nonbonding configuration a2626*2a*2, which both arise from SCF-level calculations, correspond to a realistic description of the system. Strong correlation effects require an elaborate configuration interaction (CI) treatment, which does confirm the quadruply bonding configuration as the leading term but reduces drastically the formal bond order. The importance of the presence or absence of axial ligands is not yet completely clear. From ab initio calculations3on anhydrous and dihydrated chromium formate, it was concluded that the axially situated water molecules had no major influence on the strength of the Cr-Cr bond. A more accurate configuration interaction expansion performed in the meantime4 did not modify this conclusion. However, an impressive correlation has been established experimentally between the strength of the chromium-(axial ligand) interaction and the length of the Cr-Cr bond.5 In particular, among the more recently discovered compounds are those with a so-called “supershort” bond, none of which has axial ligands, the axial access to the metal being generally impeded by bulky side groups. In these compounds the bonding configuration is likely to be closer to Dihydrated chromium acetate has already been submitted to an experimental low-temperature charge density analysis.6 A similar study a t room temperature was made on molybdenum acetate.’ Molybdenum quadruply bonded compounds behave less
a1.9
So that a better understanding of the metal-metal bonding mechanism in this class of compounds might be gained, the wave function of another complex of chromium displaying a “supershort” quadruple bond, tetrakis(pdimethylphosphoniumy1idenemethylido)dichromium, [(CH,),P(CH,),],Cr,, was calculated at a configuration interaction level. The ligand (CH,),P(CH,),, modelized into H2P(CH2),, was chosen for its simplicity (the calculation of Cr,(mhp), at the same level of accuracy would be prohibitive). Although the ligands H2P(CH2), and mhp are different, we believe that this does not affect appreciably the Cr-Cr bonding, as is attested by the similarity of the bond lengths, which differ only by 0.006 A. Experimental Section
(1) (a) Laboratoire de Cristallochimie, ERA 08 du CNRS. (b) Laboratoire de Chimie Quantique, ER 139 du CNRS. (c) To whom correspondence should be addressed at the Laboratoire de Cristallographie Biologique, Institut de Biologie Moltculaire et Cellulaire, 67084 Strasbourg CEdex, France. (2) Cotton, F. A. Acc. Chem. Res. 1978, 1 1 , 225-232. (3) Benard, M. J. A m . Chem. Soc. 1978, 100, 2354-2362. (4) Wiest, R.; Btnard, M., unpublished results. ( 5 ) Cotton, F. A.; Ilsley, W. H.; Kaim, W. J. Am. Chem. SOC.1980, 102, 3464-3474. (6) Btnard, M.; Coppens, P.; De Lucia, M. L.; Stevens, E. D. Inorg. Chem. 1980, 19, 1924-1930.
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Crystallized CrZ(mhp)&HzClz was kindly supplied by Professor F. A. Cotton. By recrystallization in chlorobenzene under argon, it was possible to grow crystals of Cr2(mhp), free of solvent molecules, as was confirmed by a room-temperature X-ray structure determination. This (7) Hino, K.; Saito, Y . ;Btnard, M. Acfa Crysfallogr.,Sect. 8 1981,837, 21 64-21 70. (8) For the chromium formate, a much more accurate CI treatment, involving all configurations generated from the set of eight Cr-Cr bonding and antibonding orbitals, yielded for the u 2 ~ 4 6leading 2 configuration a weight of only 9%., A still smaller weight was obtained by Atha et aL2* (9) Cotton, F. A.; Fanwick, P. E.; Niswander, R. H.; Sekutowski, J. C. J. Am. Chem. SOC.1978, 100, 4725-4732.
0 1982 American Chemical Society
1502 J. Am. Chem. Soc., Vol. 104, No. 26, 1982 Table I. Crystallographic Data
Mitschler et al. Table 111. Least-Squares Refinements
room temp
data set
74 K 1+2
space group Pi, = 2 13.637 10.570 8.748 78.22 102.26 94.24 1205.6 1.478
a/.&
bla c/A
p/deg ride5
v la D calcd/(g/Cm31
13.459 (2) 10.537 (2) 8.693 (1) 78.36 (2) 102.01 (2) 94.34 (2) 1180.2 (5) 1.509
none rejectn criterion no. of reflctns considered ( N ) 8515 no. of parameters @) 403 R ( F ) = Z lFo-Fcl/ZIF,I 0.050 R,(Fz)= [ Z w ( F o 2- F c 2 ) z / Z ~ F 0 4 ] 1 0.093 '2 s = [ c w (Fo2 - FC2)2/(N -p ) ] lI2 2.11 scale factor 2.407 (1)
data set X radiation (sin B)/h range/A-' no. of measmts rescan condition
MoKa
